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Logical error rate in the Pauli twirling approximation.

Amara Katabarwa¹, Michael R Geller¹

¹Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA.

Scientific Reports

|October 1, 2015

Summary

This summary is machine-generated.

The Pauli twirling approximation (PTA) reliably predicts quantum error correction performance for low-distance codes. This method, simplifying complex quantum error models, overestimates logical error rates by 2-3x compared to exact simulations.

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Area of Science:

Quantum computing
Quantum error correction
Computational complexity

Background:

Efficient simulation of quantum error models is crucial for developing quantum computers.
The Gottesmann-Knill theorem provides a class of efficiently simulable error models.
Pauli twirling approximation (PTA) simplifies arbitrary quantum error channels into Pauli channels.

Purpose of the Study:

To assess the accuracy of the Pauli twirling approximation (PTA) in predicting logical error rates.
To compare PTA predictions with exact simulations of quantum error correction codes.
To evaluate PTA's reliability for realistic quantum error models.

Main Methods:

Simulated a 5-qubit quantum error correction code using a 9-qubit circuit.
Incorporated realistic decoherence and unitary gate errors into the simulation.
Applied the Pauli twirling approximation (PTA) to model the error channel.
Compared PTA-predicted logical error rates with those from exact simulations.

Main Results:

The Pauli twirling approximation (PTA) showed good agreement with exact simulations.
PTA consistently overestimated the logical error rate by a factor of 2 to 3.
The findings support PTA's utility for predicting performance in low-distance quantum error correction codes.

Conclusions:

The Pauli twirling approximation (PTA) is a reliable tool for estimating logical error rates in quantum error correction.
PTA provides a valuable, albeit slightly conservative, prediction for low-distance codes under realistic noise conditions.
Further research can explore PTA's accuracy for higher-distance codes and more complex error models.